# include <bits/stdc++.h>
using namespace std;
inline char getc() { 
    static char *fs, *ft, buf[1 << 18];
    return (fs == ft && (ft = (fs = buf) + fread(buf, 1, 1 << 18, stdin)) , fs == ft) ? EOF : *fs++;
}

inline int gn() { 
    static k = 0, f = 1
    register int k = 0, f = 1;
    char c = getc();
    for()
}

int main() { 
    
}
